help! 13. Suppose az + by = c is a linear Diophantine equation. We have found...
(1 point) In this exercise we consider the second order linear equation y" + series solution in the form y = 0. This equation has an ordinary point at x = 0 and therefore has a power y = cmx". n=0 We learned how to easily solve problems like this in several different ways but here we want to consider the power series method. (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn...
C) 41.5 D) 50.9 24 In the xy-plane, the graph of a linear equation of the form y =mx+ b and the graph of an exponential equation of the form y = ab* both contain points (1,3) and (2,4). If the point (r, s) is on the graph of the linear equation and the point (r, t) is on the graph of the exponential equation, where 0 < r< 4 and s > t,which of the following must be true?...
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*) Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u =y- transforms the Bemoulli equation into the linear equation + (1 - x)P(3)u = (1 - x)^(x). Consider the initial value problem ry' +y = -3.xy?, y(1) = 2. (a) This differential equation can be written in the form (*) with P(1) =...
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(1 point) A Bernoulli differential equation is one of the form dy + P()y= Q(Cy" (*) dr Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=yl-n transforms the Bernoulli equation into the linear equation du dac + (1 - n)P(x)u= (1 - nQ(2). Consider the initial value problem xy' +y= -6xy?, y(1) = -2. (a) This differential equation can be written in the form...
(1 point) A Bernoulli differential equation is one of the form dy dc + P(x)y= Q(x)y" Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation du dr +(1 – n)P(x)u = (1 - nQ(x). Consider the initial value problem xy + y = 3xy’, y(1) = -8. (a) This differential equation can be written in the form (*)...
Can you help answers for B & C in a linear equation ???
iat) Solve the differential equation dx 16y a. Find an implicit solution and put your answer in the following form: 8yn2-xA2/2 - constant. help (formulas) b. Find the equation of the solution through the point (x, y)-(4, 1). y sqrt(4xA2) help (equations) C. Find the equation of the solution through the point (x, y) = (0,-4). Your answer should be of the form y = f(x). help...
5. So far in our linear modeling, we have assumed that Ylz ~ NA,+Az,σ2); that is, there is a normal distribution of common variance around the regression line. Here, we change this up! Suppose that X~Unif(0, 1) and that for a given r, we know YlN(,22). (Here, the regression lne is 01z and the variance around the regression grows as r grows.) a. In R, figure out how to generate 1000 data points that follow this model and plot them....
We have found the complementary function for the given nonhomogeneous differential equation. Now we must find the particular solution, which will be based on the form of the function of x that makes the equation nonhomogeneous, g(x) = 200x2 – 78xe. The idea is that when the partial solution y, (and its derivatives) is substituted into the equation, it must be equal exactly to g(x). Therefore, we can assume the solution contains a quadratic expression and an exponential term. Assume...
In this exercise we consider the second order linear equation y" therefore has a power series solution in the form 4y = 0. This equation has an ordinary point at x = 0 and We learned how to easily solve problems like this in several different ways but here we want to consider the power series method (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn-2 for n - 2, 3, NOTE co...